We take a new logarithmic equation and this one is very similar to the previous one and but if I've set it up correctly then the answer should be a little more eh Maybe we can get a little more intuition out of it a little more understanding so we start by just seeing that there are two terms here and one term has nothing to do with X so we subtract that term on both sides of the equal sign and are left with 2 LG X is equal to 8 minus 2 which is 6 and from here we can divide out the two so we divide by 2 on both sides and get the logarithm of x is equal to 6 divided by 2 which is 3 and from here we see something that may be a little familiar We have happened to that expression here And here we ask ourselves What do we have to raise 10 to the power of to get 3 that will then be x and that will then mean that 10 raised to the power of x is equal to 3 but here we have the logarithm of x is equal to 3 so the unknown is in the logarithm and what would that tell us in terms of if we were to have written it here as an exponent it would be the same as writing that 10 to the power of 3 is equal to x and if X equals 10 to the TR and 10 to the TR equals 1000 then 1000 H must be the answer here and we are also going to find that out using Eh yes regular calculation so we put both LG x and 3 as exponents on the number 10 is equal to 10 to the third and here we get again isolated x we get X is equal to 10 to the third which is equal to 1000 so hopefully So this made some sense because writing something as a logarithm it can also be written as Eh an exponent so if you have the unknown in the logarithm then it will end up here in eh if you are going to write it as an exponent equation and then the magic comes if we know that x is equal to 1000 Why can't we then put in the original equation so we get 2 times the logarithm of x which in that case here was 1000 and so it was plus 2 so it should be equal to 8 and so we can see if it's actually true so we take and Yes we can do the same as in instead we remove 2 on both sides so we get 2 the logarithm of 1000 is equal to 8 minus 2 which is 6 and then we divide by 2 on both sides and get the logarithm of 1000 is then equal to 3 and then we know that to get 1000 we have to raise 10 to the third so the logarithm of 1000 It is actually equal to 3 so then we get to confirm that what we found out was actually true